Symbol

Name

Definition

Unit(s)

English

Metric

a

a

Slope of lift curve

1/rad, 1/deg

a₀

a0

coning angle

rad, deg

a_1s

a1s

Longitudinal flapping

ac

ac

Aerodynamic center. [airfoil]

b

b

Number of blades

b

b

Span of wing

ft.

b_1s

b1s

Lateral flapping

b_1'

b1'

Differential lateral cyclic

c

c

Chord of blade [airfoil]

ft

c

c

Damping

ft lb/rad/sec

c_crit

ccrit

Critical damping

ft lb/rad/sec

c_c

cc

Coefficient of Chord force; two-dimensional. [airfoil]

c_d

cd

Coefficient of Drag; two-dimensional. [airfoil]

c_di

cdi

Coefficient of Induced Drag; two-dimensional. [airfoil]

c_do

cdo

Coefficient of Profile Drag; two-dimensional. [airfoil]

c_l

cl

Coefficient of Lift; two-dimensional. [airfoil]

c_lMax

clMax

Maximum coefficient of Lift; two-dimensional. [airfoil]

c_m

cm

Coefficient of Moment; two-dimensional. [airfoil]

c_n

cn

Coefficient of Normal force; two-dimensional. [airfoil]

c_m0

cm0

Coefficient of Moment at zero angle of attack; two-dimensional. [airfoil]

c_m0.25

cm0.25

Coefficient of Moment about quarter chord; two-dimensional .[airfoil]

c_mac

cmac

Coefficient of Moment about aerodynamic center; two-dimensional. [airfoil]

d

d

Rotor diameter

ft

RWA

d_r

dr

Slant line distance between rotor hub centers

ft

RWA

d_s

ds

Stagger (distance between rotor axis)

ft

RWA

g

g

Rotor gap ( elevation of one rotor over another)

ft

RWA

r

r

Radius at blade element

ft

e

e

Hinge offset; for flap and for lag

ft

e

e

Oswald's efficiency factor

f

f

Equivalent flat plate area

ft²

h

h

Vertical distance (height) [Is being replaced by z]

in. ??

i

i

Incidence

rad, deg

l

l

Longitudinal distance [Is being replaced by x]

in. ??

m'

m'

Dual rotor overlap fraction. Dual rotor overlap ratio.

%

PHA

ov

ov

Overlap, twin rotors

nondimensional

RWA

q

q

Dynamic pressure

lb/ft²

r

r

Radial distance in rotor (cylindrical coordinate)

t

t

Time

sec.

t

t

Airfoil thickness

in.

v

v

Induced velocity (positive down through the disk)

ft/sec

v_ov

v_ov

Induced velocity in overlap area (positive down through the disk)

ft/sec

RWA

w

w

Disk loading. Also DL

lb/ft²

x

x

Longitudinal distance in body system (Cartesian)

ft.

x

x

Nondimensional distance along airfoil chord. [airfoil]

nondimensional

x_cp

x_cp

Location on X-axis of center of pressure as a percentage of chord from leading edge. [airfoil]

x₀

x₀

Blade root cutout

percent

y

y

Lateral distance in body system (Cartesian)

ft./in.

z

z

Vertical distance in body system (Cartesian)

ft./in.

A

A

Area

ft²

A

A

Area of wing (horizontal or vertical stabilizer, etc)

ft²

A₁

A₁

First lateral harmonic of blade flapping

rad, deg

A_one

A_one

Area of individual rotor disk

ft²

mine

AC

AC

Aerodynamic center

mine

Α_L0

AL0

Zero lift angle

rad, deg

AR

AR

Aspect ratio

A_m

A_m

Overlap area of disks

ft²

HT

A_sys

A_sys

Total effective disk area of rotor system

ft²

HT

A_b

Ab

Area of blades

ft²

AI

AI

Autorotation Index (used by Sikorsky)

ft³/lb

B

B

Tip loss factor

B₁

B₁

First longitudinal coefficient of blade flapping

rad, deg

C_D

CD

Coefficient of Drag; non dimensional

C_H

CH

Coefficient of (profile drag?); non dimensional

C_P

CP

Coefficient of Power; non dimensional

C_m

Cm

Aerodynamic moment (section moment coefficient). Positive when pulling up.

C_m1/4

Cm

Section moment coefficient about quarter chord.

C_m0.25

Cm

Section moment coefficient about quarter chord.

C_mac

Cm

Section moment coefficient about aerodynamic center.

C_nc

Cn

Normal force coefficient (@ 90º to chord)

C_Q

CQ

Coefficient of Torque; non dimensional

C_T

CT

Coefficient of Thrust; non dimensional

C_T/σ

CToverSigma

Coefficient of Thrust/Solidity [see More Helicopter Aerodynamics by Prouty, Chapter 5]; non dimensional

D

D

Diameter of rotor

ft

D

D

Drag

lb

D_e

D_e

Equivalent Drag

DL

DL

Disk loading. Also w

lb/ft²

E

E

Efflux (engine exhaust & cooling gasses)

ft³

F

F

Side force on rotor (F-force)

lb

FM

FM

Figure of merit

GW

GW

Gross weight

lb

H

H

Horizontal force on rotor (H-force). Positive aft.

lb

K

K

A constant

K_p

K_p

Feedback gain = tan δ₃

L

L

Lift

lb

M

M

Pitching moment

lb-ft

M

M

Mach number

M_∞

M_∞

Free stream Mach number (locally M = 1)

M_c

M_c

Critical Mach number

N

N

Yawing moment

lb-ft

PA

PA

Projected Area. Area of fuselage, in plan view.

ft²

PL_H

PL_H

Power loading, at hover

PL_M

PL_M

Power loading, at maximum power

Q

Q

Torque

ft lb

R

R

Rotor radius

ft

Re | RN

RN

Reynolds number [Others | Prouty]

S_β

S_β

Stiffness number

T

T

Thrust

lb

TC

TC

Center of thrust

mine

T_E

T_E

Thrust (efflux)

lb

T_P

T_P

Thrust (port rotor)

lb

T_S

T_S

Thrust (tarboard rotor)

lb

V

V

Remote velocity, Free stream velocity

ft/sec, knots

VM

VM

Angle between the two masts on an intermeshing. OBSOLETE: see Yα (which is 1/2 VM )

radian, degree

U

U

Local velocity

ft/sec, knots

X

X

Longitudinal force

lbs.

X

X

Longitudinal stability axis

Y

Y

Lateral force on rotor (H-force). Positive toward advancing side. (sideslip)

lbs.

Y

Y

Lateral stability axis

Yα

Yalpha

Lateral angle between the mast and Z-axis

radian, degree

Z

Z

Vertical force

lbs.

Z

Z

Vertical stability axis

α

alpha

Angle of attack

radian, degree

α_LO

alphaLO

Angle of attack for zero lift

radian, degree

β

beta

Blade flapping angle

radian, degree

γ_c

gammac

Climb angle

radian, degree

δ

delta

Rudder angle

degrees

δ₃

delta3

Pitch-flap coupling angle

radian, degree

ε

epsilon

Downwash angle

radian, degree

η

eta

Sidewash angle

radian, degree

η

eta

Efficiency

percentage

ζ

zeta

Blade lag angle. + is opposite of rotor rotation

radian, degree

θ

theta

Blade pitch

radian, degree

θ₀

theta0

Collective pitch angle

radian, degree

θ_T

thetaT

Blade tip pitch angle

radian, degree

θ₁

theta1

Blade twist

radian, degree

θ_1A

theta1A

Active Blade Twist

radian, degree

mine

κ_int

kappa_int

Interference-induced power factor, twin rotors

PHA

κ_OV

kappa__OV

Overlap interference factor, twin rotors

RWA

λ

lambda

Induced inflow ratio with respect to swashplate

λ΄

lambdaprime

Induced inflow ratio with respect to tip path plane.

λ_β

λ_β

Flap frequency ratio

μ

mu

Tip speed ratio (advance ratio)

non-dimensional

ρ

rho

Density of air (0.002377 slug/ft³ & 0.07648 lb/ ft³ & 1.204100  kg/m³ @ ISA)

slug/ft³ & lb/ ft³

 kg/m³

σ

sigma

Solidity of rotor

non-dimensional

σ_ABC

sigma_ABC

Solidity of Advancing Blade Concept rotor

non-dimensional

σ_T

sigma_T

Thrust-weighted solidity

non-dimensional

τ_P

τ_P

Phase delay between attitude response and control input at high frequency. Is this the same as? Δψ

second

φ

phi

Inflow angle

radian

φ

phi

Phase angle

degrees

ψ

psi

Azimuth position of blade (cylindrical coordinate) (0º aft)

radian, degree

ω_N

omegaN

Natural frequency of blade flapping

radian/second

ω_bw

omegabw

Bandwidth

radian/second

ß

Beta

Sideslip angle

radian, degree

Γ

Gamma

Circulation

radian, degree

Γ

Gamma

Control (swashplate) phase angle (may be the same as Δψ )

radian, degree

N.L.

ΔT

DeltaT

Difference of thrust between rotors. Positive value signifies that the starboard or lower is the greater.

lb.

Δψ

Deltapsi

Change in azimuth. Phase lag angle? (may be the same as Γ )

radian, degree

Θ

Theta

Helicopter pitch angle

radian, degree

Λ

Lambda

Sweep angle

radian/second

Φ

Phi

Helicopter roll angle

radian, degree

Ψ

Psi

Helicopter yaw angle

radian, degree

Ω

Omega

Rotational speed of rotor

radian/second

ΩR

OmegaR

Tip speed of rotor

ft/sec

 Subscript

b

b

Per blade

i

i

Induced

O

O

Profile

C

C

Control (used with UniCopter)

CRU

CRU

Cruse

E

E

Efflux (exhaust and cooling discharge)

F

F

Fuselage

H

H

Horizontal, Horizontal stabilizer

HOV

HOV

Hover

L

L

Local

M

M

Main rotor

P

P

Port

Q

Q

Torque

S

S

Starboard

T

T

Tail rotor

T

T

Torque

TPP

TPP

Tip path plane

V

V

Vertical, Vertical stabilizer